When I was younger we had a cat like that. Every so often we'd come home to find a head, or just a body, sitting on our front doorstep. The cat would come wandering by, sniff it, then look at us, as if to say "Here's my rent."
It was kind of eerie, not a single sound outside ever, no chirping, no chipmunks, nothing. It was like a 500 yard deadzone around our house. Too bad when the cat was like 9 something larger and a bit more mean got it